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A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the maximum length of the chain hanging from the table is _______ m.

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answer is 2.

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Detailed Solution

Mass per unit length = $λ$

$N = mg = λ (L - x) g$

${fs}_{\max} = μ_{s} N$

${fs}_{\max} = (0.5) (λ) (L - x) g$

And also ${f_{s}}_{\max} = m_{x} g$

$0.5 λ (L - x) g = λxg$

$\frac{L - x}{2} = \frac{3 x}{2} \Rightarrow x = \frac{L}{3} = \frac{6}{3} = 2 m$

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